Breaking up the indivisible to observe the implausible—particles with a fractional charge

Using numerical simulations, researchers have been able to study a new type of …

It was 1909 when Robert Millikan and Harvey Fletcher carried out their famous oil drop experiment in which they determined that the smallest unit of charge possible was 1.592x10-19 Coulombs, a value we now refer to as e, the fundamental charge (the modern accepted value is 1.602176565(35)x10-19 C). It is the magnitude of the negative charge carried by the electron, as well as the positive charge of a proton. It is also the smallest unit of charge that any stable, independent particle can possibly have—no particles can have -3/4e charge, nor can they carry +2.8e of charge—barring technicalities. A paper published in this week's edition of Science examines in detail one of the technical loopholes to the preceding statement.

We have spent a large amount of time breaking up hadrons to our heart's content, resulting in a spew of quarks, bosons, and other fundamental particles. But no particle collider could ever hope to split an electron (or other lepton) into smaller pieces, so we have no way of looking at something that is, say, one half of an electron.

But there may be a way to split up something that looks a lot like an electron. Quasiparticles are collections of fundamental particles that have an emergent behavior similar to that of a single fundamental particle. But they are not bound by the rules that govern stable individual particles.

If a quasiparticle can be sufficiently divided and separated, it becomes, in effect, a "well-defined localized object with a sharp energy-momentum dispersion relation"—in other words, an isolated particle on its own. To date, the only realized physical examples of fractionally charged quasiparticles have all existed in what are known as Hall effect materials; searches for other classes of divisible quasiparticles have so far turned up empty. Recent(-ish) theoretical predictions have pointed to the existence of a class of low temperature paramagnets, the quantum spin liquids, but nobody had produced them experimentally.

When experiments cannot do the job, science turns to its trusty friend, simulation. (In a simulation, you can define the entirely of the world, so anything is possible.) Following up on a suggestion put forth in recent theoretical papers, the authors of the Science letter attempt to carry out a large (microscopic scale) numerical simulation of hard bosons in a hexagonal lattice that is wrapped around itself in two dimensions, forming a torus.

Using a type of Monte Carlo simulation that works with quantum systems, the authors examined, in detail, the order-to-disorder transitions that took place in as the model transitioned from a superfluid state at "low temperature" to a gapped spin-liquid at "high temperature." (Like everything else, temperature is simulated in this work.)

Given the lattice structure and the Hamiltonian—a mathematical equation that allows one to compute energy from a given state of particles—within the simulation, it's possible to figure out its lowest energy state. That turned out to have three bosons sitting at some of the six points that surrounded each hexagonal cell in the lattice. That said, in physics/chemistry, just because something is energetically favorable doesn't mean that is the only way it will exist. At certain points in the simulation "defect hexagons"—those that had only two bosons—would arise.

When the "temperature" was high enough that the system was in the disordered spin-liquid state, these defects would appear in pairs—the loss of a single boson would leave two adjacent hexagons with only two bosons surrounding them. That gave the entire system a -1 charge.

At that temperature, defects could move around freely and become separated by large distances. Since the total charge on the system was -1 these, now isolated, defects in essence each carried a fractional charge of -1/2. These freely moving defect hexagons can be thought of as a quasiparticle with half odd charge. (For those who have studied semiconducting materials at some point in their life, think of these as "holes"—the vacant positively charged quasiparticles—moving throughout the material).

To understand the physics of this system, the researchers focused on the transition between the ordered superfluid state and the disordered spin-liquid state, looking at how quickly these defects could become separated. They discovered that the probability of finding a particle in the ground state was drastically different than it is in classical systems, 1.47(3) as opposed to 0.038. This means that they were looking at a new class of phase transition, which they dubbed XY* (in contrast to the more common XY phase transitions).

While this may seem to be of limited to use to anyone but a condensed matter physicist, it provides a signature that other researchers, both experimental and theoretical, can look for to "test for the existence of fractionalized excitations" (non-integer charged quasiparticles). In concluding, the authors suggest that experimentalists look at materials similar to herbertsmithite, as these be able to hold a quantum critical point in the XY* class that they discovered in their work. Having a material with this kind of critical point, they conclude, may be useful for future quantum computing applications.

(Readers of Nobel Intent will undoubtedly point out that quarks, the constituents of baryons, do carry either a +2/3e or -1/3e charge along with their respective color charge. However since they cannot exist long in unbound states, they don't count in statement that no stable, individual particle carries anything other than a quantized charge.)

Matt Ford
Matt is a contributing writer at Ars Technica, focusing on physics, astronomy, chemistry, mathematics, and engineering. When he's not writing, he works on realtime models of large-scale engineering systems. Emailzeotherm@gmail.com//Twitter@zeotherm

17 Reader Comments

In concluding, the authors suggest that experimentalists look at materials similar to herbertsmithite, as these be able to hold a quantum critical point in the XY* class that they discovered in their work.

So does this mean that the Blacklight Power guy isn't a nutjob? Serious question. All his work was based on the supposition that there were energy levels possible below the commonly accepted "ground state".

>So does this mean that the Blacklight Power guy isn't a nutjob? Serious question. All his work was based on the supposition that there were energy levels possible below the commonly accepted "ground state".

I think the states described here are *above* the ground state.

In any case, that guy is a con artist. It's his supporters who are nuts.

Given those, I just chuckle when I get people criticizing me for pointing out the flaw in assumption that matter is homogeneous across the vast expanse of the universe.

Given what we observe we should reject other observations? It doesn't work that way.

Btw, in case it isn't obvious, I am referring to the homogeneity of the CMB, which puts precise bounds on matter-energy distributions. We now _know_ that matter is homogeneous across the universe. (But not on galaxy cluster scales and less, obviously, which _is_ the scale of structure formation.)

(Readers of Nobel Intent will undoubtedly point out that quarks, the constituents of baryons, do carry either a +2/3e or -1/3e charge along with their respective color charge. However since they cannot exist long in unbound states, they don't count in statement that no stable, individual particle carries anything other than a quantized charge.)